Inverse problem for a quadratic pencil of Sturm-Liouville operators with finite-gap periodic potential on the half-line

2007 ◽  
Vol 43 (6) ◽  
pp. 737-744
Author(s):  
B. A. Babazhanov ◽  
A. B. Khasanov
Keyword(s):  
Inverse Problem ◽  
Periodic Potential ◽  
Half Line ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Liouville Operators

On the Inverse Problem for a Quadratic Pencil of Sturm-Liouville Operators with Periodic Potential

2005 ◽  
Vol 41 (3) ◽  
pp. 310-318 ◽  
Author(s):  
B. A. Babadzhanov ◽  
A. B. Khasanov ◽  
A. B. Yakhshimuratov
Keyword(s):  
Inverse Problem ◽  
Periodic Potential ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Liouville Operators

An inverse problem for Sturm–Liouville operators on the half-line with complex weights

2019 ◽  
Vol 27 (3) ◽  
pp. 439-443
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Half Line ◽  
Sturm Liouville ◽  
The Given ◽  
Complex Valued ◽  
The Uniqueness Theorem ◽  
Liouville Operators

Abstract Second order differential operators on the half-line with complex-valued weights are considered. Properties of spectral characteristics are established, and the inverse problem of recovering operator’s coefficients from the given Weyl-type function is studied. The uniqueness theorem is proved for this class of nonlinear inverse problems, and a number of examples are provided.

scholarly journals An inverse problem for Sturm-Liouville operators on the half-line having Bessel-type singularity in an interior point

2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Alexey Fedoseev
Keyword(s):  
Inverse Problem ◽  
Interior Point ◽  
Sufficient Conditions ◽  
Weyl Function ◽  
Half Line ◽  
Type Singularity ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
The Given ◽  
Liouville Operators

AbstractWe study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.

scholarly journals Necessary and sufficient conditions for the solvability of the inverse problem for non-self-adjoint pencils of Sturm-Liouville operators on the half-line

2011 ◽  
Vol 42 (3) ◽  
pp. 247-258 ◽  
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Differential Operators ◽  
Sufficient Conditions ◽  
Weyl Function ◽  
Half Line ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
Liouville Operators

Non-self-adjoint Sturm-Liouville differential operators on the half-line with a boundary condition depending polynomially on the spectral parameter are studied. We investigate the inverse problem of recovering the operator from the Weyl function. For this inverse problem we provide necessary and suffcient conditions for its solvability along with a procedure for constructing its solution by the method of spectral mappings.

scholarly journals Partial inverse problems for quadratic differential pencils on a graph with a loop

2020 ◽  
Vol 28 (3) ◽  
pp. 449-463 ◽  
Author(s):  
Natalia P. Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Spectral Characteristics ◽  
The Other ◽  
Boundary Edge ◽  
Partial Inverse ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Differential Pencils ◽  
Liouville Operators

AbstractIn this paper, partial inverse problems for the quadratic pencil of Sturm–Liouville operators on a graph with a loop are studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the loop) from spectral characteristics, while the coefficients on the other edges are known a priori. We obtain uniqueness theorems and constructive solutions for partial inverse problems.

scholarly journals On Povzner–Wienholtz-type self-adjointness results for matrix-valued Sturm–Liouville operators

2003 ◽  
Vol 133 (4) ◽  
pp. 747-758 ◽  
Author(s):  
Steve Clark ◽  
Fritz Gesztesy
Keyword(s):  
Half Line ◽  
Sturm Liouville ◽  
Image Position ◽  
Liouville Operators

We derive Povzner–Wienholtz-type self-adjointness results for m × m matrix-valued Sturm–Liouville operators in L2((a, b);R dx)m, m ∈ N, for (a, b) a half-line or R.

scholarly journals Inverse problem for Sturm-Liouville operators on a curve

2019 ◽  
Vol 50 (3) ◽  
pp. 349-359
Author(s):  
Andrey Aleksandrovich Golubkov ◽  
Yulia Vladimirovna Kuryshova
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Transfer Matrix ◽  
Liouville Equation ◽  
Inverse Spectral Problem ◽  
Rectifiable Curve ◽  
Uniqueness Of The Solution ◽  
Sturm Liouville ◽  
Discontinuity Conditions ◽  
Liouville Operators

he inverse spectral problem for the Sturm-Liouville equation with a piecewise-entire potential function and the discontinuity conditions for solutions on a rectifiable curve \(\gamma \subset \textbf{C}\) by the transfer matrix along this curve is studied. By the method of a unit transfer matrix the uniqueness of the solution to this problem is proved with the help of studying of the asymptotic behavior of the solutions to the Sturm-Liouville equation for large values of the spectral parameter module.

Solvability of an inverse problem for discontinuous Sturm–Liouville operators

2020 ◽  
Vol 44 (1) ◽  
pp. 124-139
Author(s):  
Ran Zhang ◽  
Natalia Pavlovna Bondarenko ◽  
Chuan Fu Yang
Keyword(s):  
Inverse Problem ◽  
Sturm Liouville ◽  
Liouville Operators
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